McNair — A Method in Teaching Optical Mineralogy. 293 



is used at once in accounting for the phenomena exhibited by 

 thin crystal plates between crossed nicols. It is applied next 

 to the simple cases of superposition of plates of even thick- 

 ness, then to those cases in which the plates are not of even 

 thickness. By its use the average student gains some facility 

 in predicting the phenomena which will be observed in a 

 given case, such, say, as that of an even plate over one shaped 

 like a convex lens. Afterward the method is applied to crys- 

 tal plates in convergent plane polarized light and perhaps the 

 most conspicuous example of its usefulness lies in its applica- 

 tion to the distinction between positive and negative crystals 

 in the convergent beam of plane polarized light. 



Fig. 1. 



Let fig. 1 represent a central section through the converg- 

 ent cone which traverses a plate cut perpendicular to the 

 acute bisectrix. If the crystal is positive, this acute bisectrix 

 is C, the direction of minimum elasticity. If for each ray 

 direction the ellipsoid is constructed, and the section perpen- 

 dicular to the ray is cut, the elliptical sections will appear in 

 this figure only as traces marked E„ E 3 , etc. If now a dia- 

 grammatic plan be made on the assumption that the above 

 section coincides with the axial plane, and, for brevity, with 

 that plane in "the 45° position", and if the ellipses be dia- 

 grammed on this in their full area, that is, if each be tipped 

 into the plane of the diagram before being drawn, we shall 

 obtain something like fig. 2. On this figure lines represent- 

 ing the position of the hyperbola have been drawn to enable 

 it to be referred to the biaxial interference picture, and the 



